Consider the case where we have a rectangle of side lengths 2x + 3 and 3x + 1, as shown in the figure. Class 9

Consider the case where we have a rectangle of side lengths 2x + 3 and 3x + 1, as shown in the figure. Class 9

Question 1.

Consider the case where we have a rectangle of side lengths 2x + 3 and 3x + 1, as shown in the figure. What can you say about its area (2x + 3) (3x + 1)? Class 9

Fill in the blanks with the appropriate expressions to make the equation true. (px + a) (qx + b)

= (___) x² + (____) x + _________ .

Also, verify your answer using the distributive property

Answer:

i. The rectangle has side lengths 2x + 3 and 3x + 1.

The area of the rectangle is:

(2x + 3)(3x + 1) sq. units

Using algebra tiles, the rectangle consists of:

a. six x² - tiles (2x × 3x = 6x²)

b. eleven x-tiles

(2x × 1 + 3 × 3x = 2x + 9x = 11x)

c. three unit tiles (3 × 1 = 3)

Area = (2x + 3)(3x + 1) = 6x2 + 11x + 3

ii. (px + a)(qx + b) = (pq)x² + (pb + aq)x + ab

Verification:

(px + a)(qx + b) = px(qx + b) + a(qx + b)

= pqx² + pbx + aqx + ab

= pqx² + (pb + aq)x + ab